On the backward uniqueness property for the heat equation in two-dimensional conical domains
In this article we deal with the backward uniqueness property of the heat equation in conical domains in two spatial dimensions via Carleman inequality techniques. Using a microlocal interpretation of the pseudoconvexity condition, we improve the bounds of Šverák and Li (Commun. Partial Differ. Eq...
Gespeichert in:
| 1. Verfasser: | |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
12 June 2015
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| In: |
Manuscripta mathematica
Year: 2015, Jahrgang: 147, Heft: 3, Pages: 415-436 |
| ISSN: | 1432-1785 |
| DOI: | 10.1007/s00229-015-0764-4 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1007/s00229-015-0764-4
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| Verfasserangaben: | Angkana Rüland |
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| 520 | |a In this article we deal with the backward uniqueness property of the heat equation in conical domains in two spatial dimensions via Carleman inequality techniques. Using a microlocal interpretation of the pseudoconvexity condition, we improve the bounds of Šverák and Li (Commun. Partial Differ. Equ. 37(8):1414-1429, 2012) on the minimal angle in which the backward uniqueness property is displayed: We reach angles of slightly less than $${95^{\circ}}$$. Via two-dimensional limiting Carleman weights we obtain the uniqueness of possible controls of the heat equation with lower order perturbations in conical domains with opening angles larger than $${90^{\circ}}$$. | ||
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